scholarly journals Optimal heat kernel bounds under logarithmic Sobolev inequalities

1997 ◽  
Vol 1 ◽  
pp. 391-407 ◽  
Author(s):  
Dominique Bakry ◽  
Daniel Concordet ◽  
Michel Ledoux
Keyword(s):  
Heat Kernel ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities ◽  
Optimal Heat ◽  
Kernel Bounds

scholarly journals Erratum to “Global heat kernel bounds via desingularizing weights”

2005 ◽  
Vol 220 (1) ◽  
pp. 238-239
Author(s):  
Pierre D. Milman ◽  
Yu.A. Semenov
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds

BEYOND STRONG SUBADDITIVITY? IMPROVED BOUNDS ON THE CONTRACTION OF GENERALIZED RELATIVE ENTROPY

1994 ◽  
Vol 06 (05a) ◽  
pp. 1147-1161 ◽  
Author(s):  
MARY BETH RUSKAI
Keyword(s):  
Relative Entropy ◽  
Discrete Case ◽  
Sobolev Inequalities ◽  
Completely Positive ◽  
Logarithmic Sobolev Inequalities ◽  
Strong Subadditivity

New bounds are given on the contraction of certain generalized forms of the relative entropy of two positive semi-definite operators under completely positive mappings. In addition, several conjectures are presented, one of which would give a strengthening of strong subadditivity. As an application of these bounds in the classical discrete case, a new proof of 2-point logarithmic Sobolev inequalities is presented in an Appendix.

scholarly journals Heat kernel bounds on manifolds with cusps

1987 ◽  
Vol 75 (2) ◽  
pp. 311-322 ◽  
Author(s):  
E.B Davies ◽  
N Mandouvalos
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds
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